From data to structure: Construction, breakdown, and reconstruction of an empirical representation in a black-box RC circuit
Abstract
In introductory physics laboratories, a central instructional goal is to help students construct, evaluate, and revise mathematical representations from experimental data rather than apply given formulas. We present a guided data-driven activity in which an RC circuit is treated as a black box defined through observable input-output relations. Experimental and graphical procedures are provided, while standard RC circuit theory is initially withheld. Students first examine discharging data obtained under different nominal values of R and C. They rescale time using T=t/RC and compare the normalized voltage v=V/E across circuit conditions, bringing the discharging data closer to a common trajectory. Graphical linearization through a plot of lnv versus T provides a basis for proposing an empirical representation and allows RC to be interpreted as a time scale rather than being assigned that meaning a priori. When the representation proposed for discharging is tested with charging data, logarithmic linearity is lost despite the continued organization of the data by T. Replacing v with the distance from the steady state, 1-v, restores linearity, and the resulting linear relation provides a basis for proposing a revised representation for charging. The activity thus uses a familiar physical system to make representation construction, breakdown, and reconstruction experimentally explicit. It also emphasizes that an empirical representation must be accompanied by a specified domain of validity and that standard circuit theory can be introduced a posteriori to interpret the physical meanings that emerge from representational constraints.
Related
- Representation Transitions Reveal Predictive Structure in Complex Systems: A Trajectory-Level Reconstruction in a Critical System
- Comprehensive reconstruction of collider events with hypergraph representation learning and graph-conditioned diffusion
- Graph construction in QUBO-based recursive phylogenetic tree reconstruction
- Amplitude structure of 3→ 3 scattering in a Mandelstam variable representation
- AlterSeeK-Path: Systematic construction of generalized band-structure paths for displaying altermagnetic spin splitting
BibTeX
@misc{kushida2026from,
title = {{From data to structure: Construction, breakdown, and reconstruction of an empirical representation in a black-box RC circuit}},
author = {Kazumasa Kushida},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08792},
eprint = {2609.08792},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08792},
}
RIS
TY - UNPB
TI - From data to structure: Construction, breakdown, and reconstruction of an empirical representation in a black-box RC circuit
AU - Kazumasa Kushida
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08792
UR - https://arxiv.org/abs/2609.08792
AB - In introductory physics laboratories, a central instructional goal is to help students construct, evaluate, and revise mathematical representations from experimental data rather than apply given formulas. We present a guided data-driven activity in which an RC circuit is treated as a black box defined through observable input-output relations. Experimental and graphical procedures are provided, while standard RC circuit theory is initially withheld. Students first examine discharging data obtained under different nominal values of R and C. They rescale time using T=t/RC and compare the normalized voltage v=V/E across circuit conditions, bringing the discharging data closer to a common trajectory. Graphical linearization through a plot of lnv versus T provides a basis for proposing an empirical representation and allows RC to be interpreted as a time scale rather than being assigned that meaning a priori. When the representation proposed for discharging is tested with charging data, logarithmic linearity is lost despite the continued organization of the data by T. Replacing v with the distance from the steady state, 1-v, restores linearity, and the resulting linear relation provides a basis for proposing a revised representation for charging. The activity thus uses a familiar physical system to make representation construction, breakdown, and reconstruction experimentally explicit. It also emphasizes that an empirical representation must be accompanied by a specified domain of validity and that standard circuit theory can be introduced a posteriori to interpret the physical meanings that emerge from representational constraints.
ER -